The reason I have for considering such a system is in fact to reduce exposure. I don't use chemicals to remove glue, and I sure as hell don't like being exposed to the fumes while applying tubular glue. If it takes a few extra minutes to mask and prep, then I am absolutely in.
As for clogging at the spray nozzle, 3M, Scotch and a bunch of others seem to have it figured out. Chemists are a sharp lot.
The plugs could be made of teflon and shaped conically, as to provide a slight interference fit. For the thin film needed per layer, there will be no issue with their removal and subsequent cleaning. Removing a set of plugs should take no more than a minute at most.
The solvents, solubilizers, and stabilizers you'd have to add to the adhesive to make it sprayable would be a lot worse than the little bit of exposure you'd get from using a brush and a tube of Mastik.
And note that European volatile organic emissions standards have driven a couple reformulations of Mastik One anyway to reduce or eliminate the problematic compounds you are trying to avoid anyway.